Loaded pin weight will determine if you are "forced" into a dually or can get the job done with a SRW. When we purchased our 2017 BH3575el, we picked a model with a lighter 2435 lbs of dry pin weight. We towed it to Arizona and back from Washington twice with our 2015 RAM 3500 SRW 4x4 Short Box and had trailer and truck loaded heavy as we were full timing in it at the time. We made all our weight numbers.
I do not believe there is a current gas truck rated to tow a trailer your size/weight.
Maybe someone will be along and provide their loaded pin weight for your model.
So as others have said, you need a 350/3500 Diesel, and need more info regarding projected loaded pin weight to determine the number of tires under the back of the TV.
Based on this:
https://www.rvusa.com/rv-guide/2011-heartland-bighorn-fifth-wheel-floorplan-bh-3610re-tr2730
That model has a listed lighter 2115 lbs of dry pin weight. So it should be towable with the latest generation SRW 350/3500 trucks. Truck manufactures in the last few years have upped their game with better frames, running gear, and wheels and tires(I prefer the 18" wheels and tires over the 20"). Their tow ratings reflect these improvements.
Chris