<PAGE>   1
                                                                    EXHIBIT 3.11


            AMENDED AND RESTATED LIMITED LIABILITY COMPANY AGREEMENT

                                       OF

                        RENAISSANCE MEDIA (TENNESSEE) LLC

                     (A DELAWARE LIMITED LIABILITY COMPANY)


         This FIRST AMENDED AND RESTATED LIMITED LIABILITY COMPANY AGREEMENT OF
RENAISANCE MEDIA (TENNESSEE) LLC (this "Agreement"), is entered into as of April
29, 1999 by Renaissance Media Group LLC, a Delaware limited liability company
("Member") as the sole member of Renaissance Media (Tennessee) LLC, a Delaware
limited liability company (the "Company), as a complete amendment and
restatement of Limited Liability Agreement of the Company dated March 20, 1998.

         In consideration of the terms and provisions set forth herein, the
benefits to be gained by the performance thereof and other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, the
parties hereby agree as follows:

         SECTION 1. General.

         (a) Effective as of the date and time of filing of the Certificate of
Formation (the "Certificate") in the office of the Secretary of State of the
State of Delaware, the parties hereby form a limited liability company under the
Delaware Limited Liability Company Act. Except as expressly provided herein, the
rights and obligations of the members in connection with the regulation and
management of the Company shall be governed by the Delaware Limited Liability
Company Act (6 Del.C. Section 18-101, et. seq.) (the "Delaware Limited Liability
Company Act").

         (b) The name of the Company shall be "Renaissance Media (Tennessee)
LLC". The business of the Company shall be conducted under such name or any
other name or names that the Manager shall determine from time to time.

         (c) The address of the registered office of the Company in the State of
Delaware shall be c/o CorpAmerica, Inc., 30 Old Rudnick Lane, Dover, Delaware
19901. The name and address of the registered agent for service of process on
the Company in the State of Delaware shall be CorpAmerica, Inc., 30 Old Rudnick
Lane, Dover, Delaware 19901. The registered office or registered agent of the
Company may be changed from time to time by the Manager.

         (d) The principal place of business of the Company shall be at 12444
Powerscourt Drive, Suite 400, St. Louis, MO 63131. At any time, the Manager may
change the location of the Company's principal place of business.

         (e) The term of the Company will commence on the date of the filing of
the Certificate in the office of the Secretary of State of the State of
Delaware, and will continue and have perpetual existence until dissolved and its
affairs wound up in accordance with the provisions of this Agreement.


<PAGE>   2

         (f) The execution of the Certificate by Charter and the filing thereof
in the office of the Secretary of State of the State of Delaware, are hereby
ratified, confirmed and approved by the members.

         (g) The Manager shall cause the Company to be qualified, formed or
registered under assumed or fictitious name statutes or similar laws in any
jurisdiction in which the Company transacts business in which such
qualification, formation or registration is required or desirable. The Manager,
as an authorized person within the meaning of the Delaware Limited Liability
Company Act, shall execute, deliver and file any certificates (and any
amendments and/or restatements thereof) necessary for the Company to qualify to
do business in a jurisdiction in which the Company may wish to conduct business.

         SECTION 2. Purposes. The Company is formed for the object and purpose
of, and the nature of the business to be conducted by the Company is, engaging
in any lawful act or activity for which limited liability companies may be
formed under the Delaware Limited Liability Company Act and engaging in any and
all activities necessary, convenient, desirable or incidental to the foregoing.

         SECTION 3. Powers. The Company shall have all powers necessary,
appropriate or incidental to the accomplishment of its purposes and all other
powers conferred upon a limited liability company pursuant to the Delaware
Limited Liability Company Act.

         SECTION 4. Management.

         (a) Management by Managers. The Members hereby unanimously elect
Charter Communications, Inc. ("CCI"), a Delaware corporation, or its
successor-in-interest, as the Company's Manager. CCI shall be the Manager until
the Members unanimously elect otherwise. No additional person may be elected as
Manager without the unanimous approval of the Members. Except as otherwise
required by applicable law and as provided below with respect to the Board of
Directors, the powers of the Company shall at all times be exercised by or under
the authority of, and the business, property and affairs of the Company shall be
managed by, or under the direction of, the Manager.

         The Manager shall be authorized to elect, remove or replace directors
and officers of the Company, who shall have such authority with respect to the
management of the business and affairs of the Company as set forth herein or as
otherwise specified by the Manager in the resolution or resolutions pursuant to
which such directors or officers were elected.

         Except as otherwise required by applicable law, CCI, in its capacity as
Manager, shall be authorized to execute or endorse any check, draft, evidence of
indebtedness, instrument, obligation, note, mortgage, contract, agreement,
certificate or other document on behalf of the Company.

         No annual or regular meetings of the Manager or the members are
required. The Manager may, by written consent, take any action which it is
otherwise required or permitted to take at a meeting.

         (b) Board of Directors.


                                      -2-

<PAGE>   3

                   i)    Notwithstanding paragraph (a) above, the Manager may
delegate its power to manage the business of the Company to a Board of Directors
(the "Board") which, subject to the limitations set forth below, shall have the
authority to exercise all such powers of the Company and do all such lawful acts
and things as may be done by a manager of a limited liability company under the
Delaware Limited Liability Company Act and as are not by statute, by the
Certificate, or by this Agreement directed or required to be exercised or done
by the Manager. The rights and duties of the members of the Board may not be
assigned or delegated to any person or entity.

                   ii)   Except as otherwise provided herein, members of the 
Board shall possess and may exercise all the powers and privileges and shall
have all of the obligations and duties to the Company and the Members granted to
or imposed on directors of a corporation organized under the laws of the State
of Delaware.

                   iii)  The number of directors shall initially be one (1),
which number may be changed from time to time by the Manager. The initial
director shall be Jerald L. Kent.

                   iv)   Each director shall be appointed by the Manager and 
shall serve in such capacity until the earlier of his resignation, removal or
replacement by the Manager.

                   v)    No director shall be entitled to any compensation for
serving as a director. No fee shall be paid to any director for attendance at
any meeting of the Board; provided, however, that the Company may reimburse
directors for the actual reasonable costs incurred in such attendance.

         (c) Consent Required. The affirmative vote, approval, consent or
ratification of the Manager shall be required to:

                   i)    alter the primary purposes of the Company as set forth 
in Section 2;

                   ii)   issue membership interests in the Company to any Person
and admit such Person as a Member;

                   iii)  do any act in contravention of this Agreement or any
resolution of the Members, or cause the Company to engage in any business not
authorized by the Certificate or the terms of this Agreement or that which would
make it impossible to carry on the usual course of business of the Company;

                   iv)   enter into or amend any agreement which provides for 
the management of the business or affairs of the Company by a person other than
the Manager;

                   v)    change or reorganize the Company into any other legal
form;

                   vi)   amend this Agreement;

                   vii)  approve a merger or consolidation with another Person;


                                      -3-

<PAGE>   4

                   viii) sell all or substantially all of the assets of the
Company;

                   ix)   change the status of the Company from one in which
management is vested in the Manager to one in which management is vested in the
Members or in any other manager, other than as may be delegated to the Board and
the officers hereunder;

                   x)    possess any Company property or assign the rights of 
the Company in specific Company property for other than a Company purpose;

                   xi)   operate the Company in such a manner that the Company
becomes an investment company" for purposes of the Investment Company Act of
1940;

                   xii)  except as otherwise provided or contemplated herein,
enter into any agreement to acquire property or services from any Person who is
a director or officer;

                   xiii) settle any litigation or arbitration with any third
party, any Member, or any Affiliate of any Member, except for any litigation or
arbitration brought or defended in the ordinary course of business where the
present value of the total settlement amount or damages will exceed $5,000,000;

                   xiv)  materially change any of the tax reporting positions or
elections of the Company;

                   xv)   make or commit to any expenditures which, individually 
or in the aggregate, exceed or are reasonably expected to exceed the Company's
total budget (as approved by the Manager) by the greater of 5% of such budget or
Five Million Dollars ($5,000,000); or

                   xvi)  make or incur any secured or unsecured indebtedness
which individually or in the aggregate exceeds Five Million Dollars
($5,000,000), provided that this restriction shall not apply to (i) any
refinancing of or amendment to existing indebtedness which does increase total
borrowing, (ii) any indebtedness to (or guarantee of indebtedness of) any
company controlled by or under common control with the Company ("Intercompany
Indebtedness"), (iii) the pledge of any assets to support any otherwise
permissible indebtedness of the Company or any Intercompany Indebtedness or (iv)
indebtedness necessary to finance a transaction or purchase approved by he
Manager.

         (d) Board of Director Meetings.

                   i)    Regular Meetings. Regular meetings of the Board may be
held without notice at such time and at such place as shall from time to time be
determined by the Board, but not less often than annually.

                   ii)   Special Meetings. Special meetings of the Board may be
called by the president or any member of the Board on twenty-four (24) hours'
notice to each director; special meetings shall be called by the president or
secretary in like manner and on like notice on the written request of Members
holding a majority of the Common Units held by all Members. Notice of a special
meeting may be given by facsimile.


                                      -4-

<PAGE>   5

                   iii)  Telephonic Meetings. Members of the Board may
participate in any regular or special meeting of the Board, by means of
conference telephone or similar communications equipment, by means of which all
persons participating in the meeting can hear each other. Participation in a
meeting pursuant to this Section 4.4(c) will constitute presence in person at
such meeting.

                   iv)   Quorum. Subject to the provisions of Section 4.3, at 
all meetings of the Board, a majority of the directors shall constitute a quorum
for the transaction of business, and the act of a majority of the directors
present at any meeting at which there is a quorum shall be the act of the Board,
except as may be otherwise specifically provided by statute, the Certificate or
this Agreement. If a quorum is not present at any meeting of the Board, the
directors present thereat may adjourn the meeting from time to time until a
quorum shall be present. Notice of such adjournment shall be given to any
director not present at such meeting.

                   v)    Action Without Meeting. Unless otherwise restricted by 
the Certificate of Formation or this Agreement, any action required or permitted
to be taken at any meeting of the Board may be taken without a meeting if all
members of the Board consent thereto in writing and such written consent is
filed with die minutes of proceedings of the Board.

         (e) Board's Duty of Care. The Board's duty of care in the discharge of
its duties to the Company and the Members is limited to discharging its duties
pursuant to this Agreement in good faith, with the care a corporate director of
like position would exercise under similar circumstances, in the manner it
reasonably believes to be in the best interests of the Company. In discharging
its duties, the Board shall not be liable to the Company or to any Member for
any mistake or error in judgment or for any act or omission believed in good
faith to be within the scope of authority conferred by this Agreement or
approved by the Manager.

         SECTION 5. Officers.

         (a) Officers. The officers shall be a President, a Treasurer and a
Secretary, and such other additional officers, including a Chairman of the
Board, one or more Chairmen, Vice Presidents, Assistant Secretaries and
Assistant Treasurers as the Board, the Manager or the President may from time to
time elect. Any two or more offices may be held by the same individual.

         (b) Election and Term. The President, Treasurer and Secretary shall be
elected by and shall hold office at the pleasure of the Board or the Manager.
The Board, the Manager or the President may elect such other officers and agents
as it shall deem desirable, who shall hold office at the pleasure of the Board,
the Manager or the President, and who shall have such authority and shall
perform such duties as from time to time shall be prescribed by the Board, the
Manager or the President.

         (c) Removal. Any officer may be removed by the affirmative vote of the
Manager or the affirmative vote of at least a majority of the directors then in
office, with or without cause, for any reason or for no reason. Any officer
other than the President, the Treasurer or the Secretary may be removed by the
President, with or without cause, for any reason or for no reason.

         (d) Duties and Authority of Officers.



                                      -5-

<PAGE>   6

                   i)    President. The President shall be the chief executive
officer and (if no other person has been appointed as such) the chief operating
officer of the Company; shall preside at all meetings of the Members and
directors; shall have general supervision and active management of the business
and finances of the Company; shall see that all orders and resolutions of the
Board or the Manager are carried into effect; subject, however, to the right of
the directors to delegate any specific powers to any other officer or officers.
In the absence of direction by the Board or Manager to the contrary, the
President shall have the power to vote all securities held by the Company and to
issue proxies therefor. In the absence or disability of the President, any
Chairman (if any) or, if there is no Chairman, the most senior available officer
appointed by the Board or the Manager shall perform the duties and exercise the
powers of the President with the same force and effect as if performed by the
President, and shall be subject to all restrictions imposed upon him.

                   ii)   Vice President. Each Vice President, if any, shall
perform such duties as shall be assigned to him or her and shall exercise such
powers as may be granted to him or her by the Manager, the Board or by the
President of the Company. In the absence of direction by the Board, the Manager
or the President to the contrary, the any Senior Vice President shall have the
power to vote all securities held by the Company and to issue proxies therefor.

                   iii)  The Secretary. The Secretary shall give, or cause to be
given, a notice as required of all meetings of the Members and of the Board. The
Secretary shall keep or cause to be kept, at the principal executive office of
the Company or such other place as the Board may direct, a book of minutes of
all meetings and actions of Directors and Members. The minutes shall show the
time and place of each meeting, whether regular or special (and, if special, how
authorized and the notice given), the names of those present at directors'
meetings, the number of shares present or represented at shareholders' meetings,
and the proceedings thereof. The Secretary shall perform such other duties as
may be prescribed from time to time by the Manager or the Board.

                   iv)   The Treasurer. The Treasurer shall have custody of the
Company funds and securities and shall keep or cause to be kept full and
accurate accounts of receipts and disbursements in books of the Company to be
maintained for such purpose; shall deposit all moneys and other valuable effects
of the Company in the name and to the credit of the Company in depositories
designated by the Manager or the Board; and shall disburse the funds of the
Company as may be ordered by the Manager or the Board.

                   v)    The Chairmen. Each Chairman, if any, shall perform such
duties as shall be assigned, and shall exercise such powers as may be granted to
him or her by the Manager or the Board.

         SECTION 6. Members.

         (a) The members of the Company shall be set forth on Exhibit A hereto.
Other persons may be admitted as members from time to time pursuant to the
provisions of this Agreement.


                                      -6-

<PAGE>   7

         (b) No member shall be liable for the debts, liabilities and
obligations of the Company, including any debts, liabilities and obligations
under a judgment, decree or order of a court.

         (c) Neither a member nor any of its affiliates, partners, members,
directors, managers, officers or employees shall be expressly or impliedly
restricted or prohibited by virtue of this Agreement or the relationships
created hereby from engaging in other activities or business ventures of any
kind or character whatsoever. Except as otherwise agreed in writing, each member
and its affiliates, partners, members, directors, managers, officers and
employees shall have the right to conduct, or to possess a direct or indirect
ownership interest in, activities and business ventures of every type and
description, including activities and business ventures in direct competition
with the Company.

         SECTION 7. Percentage Interests. Each member has heretofore made the
capital contribution or has the percentage interest described in the Limited
Liability Company Agreement dated March 20, 1998. As of the date hereof, the
Percentage Interests or number of membership units held by each Member shall be
as set forth in Exhibit A attached hereto.

         SECTION 8. Distributions. The Company may from time to time distribute
to the members such amounts in cash and other assets as shall be determined by
the members. Each such distribution, including liquidating distributions, shall
be divided among the members in accordance with their Percentage Interests.

         SECTION 9. Allocations. The profits and losses of the Company shall be
allocated to the members in accordance with their Percentage Interests or number
of membership units.

         SECTION 10. Dissolution; Winding Up.

         (a) The Company shall be dissolved upon (i) the adoption of a plan of
dissolution by the members or (ii) the occurrence of any event required to cause
the dissolution of the Company under the Delaware Limited Liability Company Act.

         (b) Any dissolution of the Company shall be effective as of the date on
which the event occurs giving rise to such dissolution, but the Company shall
not terminate unless and until all its affairs have been wound up and its assets
distributed in accordance with the provisions of the Delaware Limited Liability
Company Act.

         (c) Upon dissolution of the Company, the Company shall continue solely
for the purposes of winding up its business and affairs as soon as reasonably
practicable. Promptly after the dissolution of the Company, the Manager shall
immediately commence to wind up the affairs of the Company in accordance with
the provisions of this Agreement and the Delaware Limited Liability Company Act.
In winding up the business and affairs of the Company, the Manager may take any
and all actions that they determine in its sole discretion to be in the best
interests of the members, including, but not limited to, any actions relating to
(i) causing written notice by registered or certified mail of the Company's
intention to dissolve to be mailed to each known creditor of and claimant
against the Company, (ii) the payment, settlement or compromise of existing
claims against the Company, (iii) the making of reasonable provisions for
payment of contingent claims against the Company and (iv) the sale or
disposition of the properties and 

                                      -7-

<PAGE>   8
assets of the Company. It is expressly understood and agreed that a reasonable
time shall be allowed for the orderly liquidation of the assets of the Company
and the satisfaction of claims against the Company so as to enable the Manager
to minimize the losses that may result from a liquidation.

         SECTION 11. Transfer. For so long as the Company has more than one
member, no member shall transfer (whether by sale, assignment, gift, pledge,
hypothecation, mortgage, exchange or otherwise) all or any part of his, her or
its limited liability company interest in the Company to any other person
without the prior written consent of each of the other members; provided,
however, that this Section 11 shall not restrict the ability of any member to
transfer (at any time) all or a portion of its limited liability company
interest in the Company to another member. Upon the transfer of a member's
limited liability company interest, the Manager shall provide notice of such
transfer to each of the other members and shall amend Exhibit A hereto to
reflect the transfer.

         SECTION 12. Admission of Additional Members. The admission of
additional members to the Company shall be accomplished by the amendment of this
Agreement and, if required by the Delaware Limited Liability Company Act.

         SECTION 13. Tax Matters. The members agree that, so long as the Company
has more than one member, it is intended that the Company shall be treated as a
partnership for purposes of United States federal, state and local income tax
laws, and further agree not to take any position or make any election, in a tax
return or otherwise, inconsistent therewith. So long as the Company is a
partnership for federal income tax purposes, the "tax matters partner" of the
Company (the "Tax Matters Member") for purposes of section 6231(a)(7) of the
Internal Revenue Code of 1986, as amended, shall be as set forth in Exhibit A,
attached hereto. The Tax Matters Member shall have the power to manage and
control, on behalf of the Company, any administrative proceeding at the Company
level with the Internal Revenue Service relating to the determination of any
item of Company income, gain, loss, deduction or credit for federal income tax
purposes. In the event that the Company becomes a sole member entity, it is
intended that for federal income tax purposes its assets be deemed to be owned
by the sole member in accordance with the applicable Treasury Regulations.

         SECTION 14. Exculpation and Indemnification.

         (a) Neither the members, the Manager, the directors, their affiliates,
nor any person who at any time shall serve, or shall have served, as a director,
officer, employee or other agent of any member or any such affiliate and who, in
such capacity, shall engage, or shall have engaged, in activities on behalf of
the Company (a "Specified Agent") shall be liable, in damages or otherwise, to
the Company or to any member for, and neither the Company nor any member shall
take any action against such members, their affiliates or any Specified Agent,
in respect of any loss which arises out of any acts or omissions performed or
omitted by it pursuant to the authority granted by this Agreement, or otherwise
performed on behalf of the Company, if such member, such affiliate, or such
Specified Agent, as applicable, in good faith, determined that such course of
conduct was in the best interests of the Company. Each member shall look solely
to the assets of the Company for return of his, her or its investment, and if
the property of the Company remaining after the discharge of the debts and
liabilities of the Company is insufficient to return such investment, each
member shall have no recourse against the Company, the other 


                                      -8-
<PAGE>   9

members or their affiliates, except as expressly provided herein; provided,
however, that the foregoing shall not relieve any member of any fiduciary duty
or duty of fair dealing to the other members that it may have under applicable
law.

         (b) In any threatened, pending or completed claim, action, suit or
proceeding to which a member, any of such member's affiliates, or any Specified
Agent was or is a party or is threatened to be made a party by reason of the
fact that such person is or was engaged in activities on behalf of the Company,
including without limitation any action or proceeding brought under the
Securities Act of 1933, as amended, against a member, any of such member's
affiliates, or any Specified Agent relating to the Company, the Company shall
indemnify and hold harmless the members, any such affiliates, and any such
Specified Agents against losses, damages, expenses (including attorneys' fees),
judgments and amounts paid in settlement actually and reasonably incurred by or
in connection with such claim, action, suit or proceeding; provided, however,
that none of the members, any of their affiliates or any Specified Agent shall
be indemnified for actions constituting bad faith, willful misconduct, or fraud.
Any act or omission by any member, any of such member's affiliates or any
Specified Agent, if done in reliance upon the opinion of independent legal
counsel or public accountants selected with reasonable care by such member, such
affiliate or such Specified Agent, as applicable, shall not constitute bad
faith, willful misconduct, or fraud on the part of such member, affiliate or
Specified Agent.

         (c) The termination of any claim, action, suit or proceeding by
judgment, order or settlement shall not, of itself, create a presumption that
any act or failure to act by a member, such member's affiliate or any Specified
Agent constituted bad faith, willful misconduct or fraud under this Agreement.

         (d) Any such indemnification under this Section 13 shall be recoverable
only out of the assets of the Company and not from the members.

         SECTION 15. Miscellaneous.

         (a) A member's limited liability company interest may be evidenced by a
certificate of limited liability company interest executed by the Manager or an
officer and in substantially the form attached hereto as Exhibit B (or in such
other form as the Manager may approve).

         (b) The terms and provisions set forth in this Agreement may be
amended, and compliance with any term or provision set forth herein may be
waived, only by a written instrument executed by each member. No failure or
delay on the part of any member in exercising any right, power or privilege
granted hereunder shall operate as a waiver thereof, nor shall any single or
partial exercise of any such right, power or privilege preclude any other or
further exercise thereof or the exercise of any other right, power or privilege
granted hereunder.

         (c) This Agreement shall be binding upon and inure to the benefit of
the members and their respective successors and assigns.

         (d) This Agreement shall be governed by, and construed in accordance
with, the laws of the State of Delaware, without regard to any conflicts of law
principles that would require the application of the laws of any other
jurisdiction.


                                      -9-

<PAGE>   10

         (e) In the event that any provision contained in this Agreement shall
be held to be invalid, illegal or unenforceable for any reason, the invalidity,
illegality or unenforceability thereof shall not affect any other provision
hereof.

         (f) This Agreement may be executed in one or more counterparts, each of
which shall be deemed an original, but all of which together shall constitute
one and the same instrument.





                                      -10-
<PAGE>   11


         IN WITNESS WHEREOF, the party has caused this Agreement to be duly
executed on the date first above written.

                                    RENAISSANCE MEDIA (TENNESSEE) LLC



                                     By:     /s/Curtis S. Shaw
                                             -------------------------------
                                             Curtis S. Shaw
                                             Senior Vice President



                                      -11-

<PAGE>   12


                                    EXHIBIT A


MEMBER NAME                                 NUMBER OF UNITS/PERCENTAGE INTEREST
-----------                                 -----------------------------------


Renaissance Media Group LLC                 100%










TAX MATTERS MEMBER
------------------


Charter Communications, Inc.






                                      -12-
<PAGE>   13


                                    EXHIBIT B






                                      -13-