To solve the equation \( x^3 - 9 = 6 \), we can follow these steps:
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Add 9 to both sides of the equation:
\[ x^3 - 9 + 9 = 6 + 9 \] \[ x^3 = 15 \]
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Take the cube root of both sides:
\[ x = \sqrt[3]{15} \]
Thus, the solution to the equation \( x^3 - 9 = 6 \) is
\[ x = \sqrt[3]{15}. \]