Unfortunately IMO you may find that your Ram 1500 lacks enough Payload Capacity to support the 313RKS's loaded pin weight.
The best way to determine what your 2011 Ram can support (TT Tongue Weight or FW Pin Weight) is take your Ram to a CAT scale....., it's a simple process. Weigh your Ram "loaded" (full fuel, passengers, cargo) then subtract the CAT scale weight from your Ram's GVWR that is noted on your driver's door. The remaining weight is the available Payload Capacity you have for a TT's loaded tongue weight or a FW's loaded pin weight.
Taking the couple minutes at the CAT scale will eliminate all the guess work.
I noticed you also posted at the "Weighed my 2013 Ram today" thread, which is a good reference for what many 1/2 ton owners run into with the heavier TT's..., especially FW's.