Towing an RV is hard work, the hardest type of trailer. The tow rating is for the easiest type. An 8k V-nose boat with 8% TW for example will tow far better than a 6000 pound TT.
Towing that TT with that truck will likely be 500 pounds over GVWR, rear axle, and GCWR of the truck. Lots of people do it anyway. If you want to stay under all of those, better analysis of your truck's ratings needs to be done. Start with the tire and loading sticker for as equipped payload that
fla-gypsy posted. Subtract the weight of your family plus about 200 pounds for stuff that fills up the truck bed. Multiply by 7 for a reasonable dry RV weight.