To solve the equation \( x^3 = 343 \), you need to take the cube root of both sides.
\[ x = \sqrt[3]{343} \]
Now, calculate the cube root of 343. Since \( 7 \times 7 \times 7 = 343 \), we have:
\[ x = 7 \]
Thus, the solution to the equation \( x^3 = 343 \) is:
\[ x = 7 \]