Cardinal 3515RT is a 40-footer with 4 slides and a GVWR of 16,135 pounds. Wet and loaded hitch weight will be about 2,886 if you balance the load in the trailer to result in 18 percent pin weight.
Cardinal 3515RT
2008 F-350 SRW 4x4 CrewCab has a GVWR of 11,500 pounds, and a GCWR of 23,500 pounds.
11,500 GVWR minus 2,886 pin weight = 8,614 max weight of the wet and loaded tow vehicle before you tie onto the trailer. That's a reasonable expectation for your truck if you don't have a toolbox full of tools and three NFL linebackers in the back seat.
If you try hard, you can probably get the weight of your wet and loaded tow vehicle down to 8,614 pounds before you tie onto the trailer. So you won't be over the GVWR of the tow vehicle, which is the usual problem with trying to tow a heavy 5er with an SRW pickup.
So that leaves a max trailer weight of 14,386 without exceeding the GCWR of your tow vehicle. Your truck can handle the hitch weight with no wiggle room, but when the trailer is wet and loaded for a long trip with a 16,000 pound gross trailer weight, you're going to be straining the guts out of your tow vehicle. Stay away from mountains, or even hill country, and travel with the holding and fresh water tanks empty, and you can probably "get by" safely.
But if I'm hauling wife and kids and grandkids and great-grandkids, I would want a tow vehicle with at least 26,000 GCWR to tow that monster-size trailer. 2005-up F-350 DRW with the TowBoss pkg, or F-450 pickup. Both of those have at least a 4.30 rear axle ratio.
So one patch to help you tow that big trailer with your not-quite-enough truck is to change the ring gear and pinion in both differentials to a 4.30 ratio. That won't beef up the frame and suspension and brakes to match the duallies, but at least you won't be a rolling roadblock when climbing a big hill or a mountain pass, so it increases your safety.
(Yes, I have great-grandkids.)