Soundproofing

will Adding sheetrock directly adhered to existing wall will only mildly help your sound retarding idea - you're not providing acoustic-deadening void, or any substantive insulating system. Barring addition of sound blanket and rated double rock wall, you could rip off your side of existing rock and replace with a rock system engineered for sound retardence. More work than you probably want to do but if you are already doing something, go a bit further and do the more correct thing and get better results.

Thanks Drumbane.

Drumbane gives good advice. Your original idea will also definitely reduce the sound. They also make a thick rubber mat, which is often used in the walls and floors of sound studios and to isolate home theaters. It's very heavy (about 1 pound/square foot) and will also help if you put it on the existing wall and then cover with another layer of 5/8" sheetrock.