Suppose that $a$ and $b$ are positive real numbers such that $3\log_{101}\left(\frac{1,030,301-a-b}{3ab}\right) = 3 - 2 \log_{101}(ab)$. Find $101 - \sqrt[3]{a}-  \sqrt[3]{b}$.

Let's think step by step and output the final answer within \boxed{}.
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