Inspired by Steven Zheng

Algebra Level 3

Let

\[S_{0} = \frac{1}{2^{8}}+\frac{1}{4^{8}}+\frac{1}{6^{8}}+\ldots\]

\[S_{1} = \frac{1}{1^{8}}+\frac{1}{3^{8}}+\frac{1}{5^{8}}+\ldots\]

If \(\frac{S_{0}}{S_{1}} = \frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b?\)

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