Infinite exponent expression

Algebra Level 3

\[\dfrac{6}{7}\ + \dfrac{1^{-3}+2^{-3}+3^{-3}+4^{-3}+5^{-3}+\cdots }{1^{-3}+3^{-3}+5^{-3}+7^{-3}+9^{-3}+\cdots } = \, ? \]

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