There is an alternative to resurfacing you might want to investigate. There are methods that can be used to raise a sunken slab of virtually any size back to it's original position. You might be able to raise the slab yourself if it is not too large and heavy. You can use a pick or mattock a type of pick with one broad, flat end used for prying or digging to raise the slab high enough to add a filler material beneath it. Various materials can be used.
Sand is the easiest to work with, though small stones or gravel are also acceptable options.
You can also use concrete provided it doesn't get squeezed out by the pressure of the slab. Place a sheet of plastic under the slab over the wet concrete before lowering the slab. This will keep the new cement from sticking to the slab just in case you have to relevel it sometime in the future. Some long slabs, such as those used for concrete walks, are made in a single pour. They usually have expansion grooves cut into them at regular intervals to give the concrete a place to break neatly if stressed instead of cracking randomly.