For some positive integer \(k,\) both \(4^k\) and \(5^k\) start with the same digit \(x\) in base 10:
\[\begin{align} 4^k &= \overline{x\dots} \\\\ 5^k &= \overline{x\dots}.\end{align}\]
What is the sum of all possible values of \(x?\)

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