I'm a coin guy but you know we run across other collectibles at times, and about 10 years ago I ran across this bill and thought it was neat so I bought it. Does grading make much of a difference with these if it is circulated?
Just as in the coin realm, condition always affects value. Still, if what you are describing is a $10 FRN with eight 6s (e.g., 66666666) it will have a significant premium notwithstanding it being circulated. The series, degree of circulation, any "problems," and even the district, will also have an effect on value. Its certainly worth in the hundreds of dollars. A picture/scan is always best.
Having the note graded could increase the comfort level of live bidders at auction. However, the note you described will still carry a hefty premium whether it is graded or not.
Just to clarify gnats comment, any zeros or other numbers in the serial number would disqualify this as a "solid" serial numbers and diminish the value somewhat. 06666666 is not as good as 66666666 and not really a "solid" serial number.
I'd guess that a F-VF solid would be worth about half of what a CU solid number would be worth, but I emphasize "guess".
I'm going to see if I can scan it and post it. Thanks for the comments