Zi Song's bound

Let \( S(n)\) denote the sum of digits of the integer \(n\). Over all positive integers, the minimum and maximum values of \( \frac {S(n)}{S(5n)} \) are \(X\) and \(Y\) respectively. The value of \(X+Y\) can be written as \( \frac {a}{b} \), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

This problem is proposed by Zi Song.

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