To solve the equation \( 1 = m^3 \), we need to isolate \( m \).
To do this, we can take the cube root of both sides of the equation:
\[ m = \sqrt[3]{1} \]
Since the cube root of 1 is 1, we find:
\[ m = 1 \]
Thus, the solution is:
\[ \boxed{1} \]