Amazingly advanced

\[p(n) = \sum _{ k=1 }^{ y }{ \left\lfloor \frac { n }{ { 5 }^{ k } } \right\rfloor } \]

Given \(n,y,k\) are positive integers, \(y\) is the largest integer such that the inequality \(5^y \leq n \) is satisfied. For the function \(p(n) \) as described above, if \(p(n) = 781 \). Find the sum of all possible values of \(n\).

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