What is the value of a 1999 all copper dime?

If your coin is thinner than a normal dime, what you have is probably a "lamination error". This error occurs when the cupronickel cladding doesn't adhere and the coin is struck on the inner copper core. A double-sided lamination error is fairly uncommon so IF that's the case I would have it examined in person by a dealer who specializes in error coins. Another alternative is that it's an off-metal strike, which occurs when a planchet (blank) for a different denomination or foreign coin accidentally gets mixed in with normal dime blanks. Again, this would have to be examined by someone in person to verify. If the coin is the same size and weight as a normal dime, then the third possibility is that someone simply plated it with copper, in which case it's an altered coin with no additional numismatic value. I confess to having done the same back in high school, creating a number of "copper" nickels and dimes after learning about half-reactions in chemistry class.