you asked for the Gross Vehicle Weight thats GVW the total of the empty truck and its legel load. when rdd stated 23k, thats the empty weight, the gross weght would be 23k+10k for the load, or 33k, in your case if your truck has a wrecker walking beam then its gvw would be that of a wrecker which is about 42k accordind to tm -----260-10,
also some states say a cdl is needed if theres air for the brakes, i tryed to get a anaswer to this question when i was i ca. thay could not give me one because theres nothing about assested brakes but on the other air is involeved, i said the hell with it and didnt worry about it when driving the m52 , my 819 (tractor wrecker)weighs 35065 , i have historic plates on it, in ca. i was never stoped or ever asked if ihad a cdl i drove the m52 for 5 years, same here in ga.with the 819