#### Answer

$-13$

#### Work Step by Step

Add 3 on both sides of the equation to obtain:
$\sqrt[3]{1-2x}-3+3=0+3
\\\sqrt[3]{1-2x}=3$
Cube both sides of the equation to obtain:
$1-2x=3^3
\\1-2x=27$
Subtract 1 on both sides to obtain:
$-2x = 26$
Divide -2 to both sides of the equation to obtain:
$x=\frac{26}{-2}
\\x=-13$
Thus, the solution is $\left\{-13\right\}$.