A positive real number $x$ is such that \[
\sqrt[3]{1-x^3} + \sqrt[3]{1+x^3} = 1.
\]Find $x^6.$The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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