Check your tires that will most likely be your weakest link, you will be over the door sticker or real close. I have a 2013 chevy 2500HD(GVWR 10,000lbs) and towing a 14,000lb gooseneck trailer at 13,000lb loaded I was 150lbs under my tire capacity of 6400lbs, this was too close for me so I upgraded my wheels and tires.
You will probably find you will end up doing some suspension upgrades to make the ride better, my truck felt squishy in the rear when loaded to max weight. Best bet is to get your TV weighed loaded to go and see what capacity you have left to work with.