A method of recovering rubber from rubber-containing briquettes comprising: a. utilizing aged briquettes comprising at least one antioxidant and chopped guayule plant matter that contains bagasse, rubber, resin and less than 5 weight % leaves, wherein the briquettes have been aged for about 21-200 days after formation; b. mixing the briquettes with (i) at least one non-polar organic solvent and (ii) at least one polar organic solvent to produce a slurry where the total amount of (i) and (ii) is 50-90% by weight of the slurry, the briquettes comprise 10-50% by weight of the slurry, the slurry contains 0.5-10 weight % water, and the at least one non-polar organic solvent (i) and the at least one polar organic solvent (ii) are present in relative weight amounts of 50-90% and 10-50%, respectively; c. removing a majority of the bagasse from the slurry to produce a miscella and a first bagasse portion; d. optionally adding additional polar organic solvent, non-polar solvent or a combination thereof to the miscella to form a reduced viscosity miscella, wherein any additional polar organic solvent and non-polar organic solvent that is added is the same or different than those utilized in (a) and the amount of any additional polar organic solvent added is less than the amount that causes the rubber contained with the reduced viscosity miscella to coagulate; e. removing 80-95 weight % bagasse, based upon the total weight of bagasse present in the reduced viscosity miscella, from the miscella produced in (c) or (d) thereby forming a purified miscella and a second bagasse fraction, wherein a majority of the bagasse that is removed has a particle size of less than 105 microns; f. optionally treating the purified miscella to remove additional bagasse thereby producing a clarified rubber solution that contains 0.01-1% by weight bagasse (based on the total weight of bagasse present in the slurry) thereby producing a clarified rubber solution; g. increasing the relative amount of polar solvent as compared to non-polar solvent within the purified miscella or clarified rubber solution so as to coagulate the rubber, wherein the coagulation is controlled so that higher molecular weight rubber having a molecular weight of at least 1,000,000 grams/mole, as measured by GPC using a polystyrene standard, coagulates and lower molecular weight rubber remains in solution; and h. producing solid purified rubber from the coagulated rubber where when said solid purified rubber contains 0.8% volatile matter it also contains 0.05-0.5 weight % dirt, 0.2-1.5 weight % ash and 0.1-4 weight % resin, wherein at least (b)-(f) are conducted at a temperature or temperatures of 10-80 °C and a pressure of 35 to 1000 kPa. a. utilizing aged briquettes comprising at least one antioxidant and chopped guayule plant matter that contains bagasse, rubber, resin and less than 5 weight % leaves, wherein the briquettes have been aged for about 21-200 days after formation; b. mixing the briquettes with (i) at least one non-polar organic solvent and (ii) at least one polar organic solvent to produce a slurry where the total amount of (i) and (ii) is 50-90% by weight of the slurry, the briquettes comprise 10-50% by weight of the slurry, the slurry contains 0.5-10 weight % water, and the at least one non-polar organic solvent (i) and the at least one polar organic solvent (ii) are present in relative weight amounts of 50-90% and 10-50%, respectively; c. removing a majority of the bagasse from the slurry to produce a miscella and a first bagasse portion; d. optionally adding additional polar organic solvent, non-polar solvent or a combination thereof to the miscella to form a reduced viscosity miscella, wherein any additional polar organic solvent and non-polar organic solvent that is added is the same or different than those utilized in (a) and the amount of any additional polar organic solvent added is less than the amount that causes the rubber contained with the reduced viscosity miscella to coagulate; e. removing 80-95 weight % bagasse, based upon the total weight of bagasse present in the reduced viscosity miscella, from the miscella produced in (c) or (d) thereby forming a purified miscella and a second bagasse fraction, wherein a majority of the bagasse that is removed has a particle size of less than 105 microns; f. optionally treating the purified miscella to remove additional bagasse thereby producing a clarified rubber solution that contains 0.01-1% by weight bagasse (based on the total weight of bagasse present in the slurry) thereby producing a clarified rubber solution; g. increasing the relative amount of polar solvent as compared to non-polar solvent within the purified miscella or clarified rubber solution so as to coagulate the rubber, wherein the coagulation is controlled so that higher molecular weight rubber having a molecular weight of at least 1,000,000 grams/mole, as measured by GPC using a polystyrene standard, coagulates and lower molecular weight rubber remains in solution; and h. producing solid purified rubber from the coagulated rubber where when said solid purified rubber contains 0.8% volatile matter it also contains 0.05-0.5 weight % dirt, 0.2-1.5 weight % ash and 0.1-4 weight % resin,