Should I tow a 30' 7" 5820lb trailer with 2005 Yukon Denali XL?

I have a 6.0 3/4 ton suburban with max tow rating of 7600 pounds. The reason for the low tow rating is only the rear ratio. With a 4.10 ratios the 6.0 3/4 subs of that generation could tow 10,000 pounds. The 07 and up 3/4 subs have 1,000 pound hitch weight max, not replaceable, and are limited to max wet weights of 7000 pounds regardless gear ratios/transmissions.