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Number Theory Level pending

Let \(S_{k}\) denote the sum of digits of a number. Then, what are the two numbers m and n such that,

\(S_{k}(m^{1})\) = \(n^{1}\)

\(S_{k}(m^{2})\) = \(n^{2}\)

\(S_{k}(m^{3})\) = \(n^{3}\)

\(S_{k}(m^{4})\) = \(n^{4}\)

What is the sum of these two numbers?

Note that m,n>1

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