To find the cube root of \(-343\), you can express it mathematically as:
\[ \sqrt[3]{-343} \]
Since \(343\) is equal to \(7^3\), we can rewrite \(-343\) as:
\[ -343 = - (7^3) \]
Now, taking the cube root gives:
\[ \sqrt[3]{-343} = \sqrt[3]{- (7^3)} = -7 \]
Thus, the cube root of \(-343\) is:
\[ \boxed{-7} \]