A positive real number $x$ is such that \[
\sqrt[3]{1-x^3} + \sqrt[3]{1+x^3} = 1.
\]Find $x^6.$
Question:
A positive real number $x$ is such that \[
\sqrt[3]{1-x^3} + \sqrt[3]{1+x^3} = 1.
\]Find $x^6.$
Answer:
Let's think step by step.

user
\frac{28}{27}
A positive real number $x$ is such that \[
\sqrt[3]{1-x^3} + \sqrt[3]{1+x^3} = 1.
\]Find $x^6.$
train