My Advice
The manual has specs for every option; don't assume you have that option just because it's in the manual. Check your window sticker if you kept it, or call the dealer, give them your VIN and ask what you have. The capacity should be on a sticker attached to the hitch. My '07 V-8 Limited hitch has a max tongue weight of 730 lbs. and a max trailer weight of 7300 lbs. I don't know how yours could be different unless it's aftermarket.
5100 lbs. is already above Class III limits, so you're almost certainly going to need the load balancing hardware. If the trailer weight rating of your hitch really is 6700 lbs, that gives you about 1500 lbs. that you can safely add to the net trailer weight. That's not very much!
If that's the case, plan on going on a strict diet. Paper plates, plastic cups and utensils. Completely empty the potable, waste and gray water tanks, and leave the propane tanks behind before you travel. Water weighs about 8.4 lbs. per gallon, so the water tanks alone can add nearly a thousand pounds all by themselves. Don't forget any drinks that you might bring along. In short, if your hitch is what the manual says, don't plan on using the trailer for anything until you're unhitched and hooked up to utilities. Plan on packing your clothes into luggage, and carry them in the back seat, and do other things to keep the gross trailer weight under control. Just don't exceed the maximum gross weight (don't forget to add the tongue weight) for the tow vehicle in the process!
If it's really 7300 lbs. that gives you another 600 pounds. That should give you enough leeway to carry a single propane tank and a few gallons of water while you drive; just enough that you can use the trailer at rest areas and other places without facilities. Just don't get lazy and let the weight rise. No matter what, I see frequent trips to the scales in your future if you buy this thing.
As for the length, you're going to be as long as a semi, so extended side mirrors and very careful driving and route planning are mandatory. So is renting "
The Long, Long Trailer" starring Lucille Ball and Desi Arnaz (1953). You might want to watch it before you make the decision to buy your trailer.

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