Where does OP say what truck they have. They haven't.
No telling if as one noted, it may be limited by factory hitch...as my 05 dw Duramax was limited to 4500 or 5000 lbs, as it did not come with a hitch of any sort.
Legally speaking, OP can pull what ever they want. From a warranty and performance std that is given, pulling more wieght, or frontal area and a few other factors may make it so they have no warranty per say.
Reality, no one answering honestly knows IF the OPs TV can pull said toy hauler safely and sanely!
Marty