If you haven't found it, here is a link that member "19H F250" was referring to (large pdf file): http://www.jayco.com/pdfs/DigitalTLTowGuide2011.pdf
Your TV's Tow Rating is just the beginning...., once you confirm it please review this STICKY: http://www.jaycoowners.com/showthread.php?t=3866
Also, ignore unloaded weights, think in terms of loaded weights.
Since you already have the TV, load it up like you were heading out on a camping trip and head to the nearest CAT scale, good opportunity to start with "real weights".
Compare your TV's CAT scale rear axle weight against your TV's Rear GAWR limit (found on driver's door jam). If you have yet to mount the 15K glider hitch, add another 300lbs to the CAT weight to cover the hitch weight. Now, taking 20% (15% to 25% manufacture recommendation) of the Pinnacle 35LKTS GVWR of 15,950lbs (worst case loaded weight) gives you a pin weight of 3,190lbs.
Based on your CAT scale weights do you have enough rear axle capacity left to support the 3,190lb pin weight?? Not knowing your loading habits, it is very possible your actual loaded FW weight could be less, thus resulting in a lower pin weight.
Hope this helps.