Will my truck pull this TT safely?

The trailer I am considering is 29' in length with a GVWR of 9,680 lbs and a UVW of 6,966.

Need more information. Use 13 percent of the trailers gross weight for your calculations on tongue weight. That would be 1260 pounds. Does your truck have a receiver that is rated that high and does your truck have the payload to accommodate that weight and all the weight of people, dogs, bicycles, kayaks, firewood, tools, bbq, chairs, etc. If you have a three quarter ton or one ton it is probably a no brainier. If you have a half ton you may be at the limit. Unless, of course, you have the mighty half ton Toyota Tundra, then you can pull your 173,000 pound space shuttle around the neighborhood impressing all your neighbors.