Infinite exponent expression

Algebra Level 3

67 +13+23+33+43+53+13+33+53+73+93+=?\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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