\(m\) is a positive integer such that \(\overline{mm} \div m^2\) is equal to some integer, \(k\). What is the sum of all possible values of \(k\)?

**Details and assumptions**:

\(\overline{aa}\) means the number obtained by writing \(a\) twice. For example if \(a=103\), then \(\overline{aa}=103103\).

This problem appeared in the TOT 2004.

This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.

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