Fraction Sum Reciprocal Product Power

Level pending

If the value of

\( \LARGE \displaystyle \frac {\left ( \frac {1}{1^2} + \frac {1}{2^2} + \frac {1}{3^2} + \ldots \right) \left ( \frac {1}{1^4} + \frac {1}{2^4} + \frac {1}{3^4} + \ldots \right) }{ \frac {1}{1^6} + \frac {1}{2^6} + \frac {1}{3^6} + \ldots } \)

is in the form of \( \frac {a}{b} \) for coprime positive integers \(a,b\). What is the value of \(a+b\)?

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