#### Answer

The solution is $\left\{0\right\}$.

#### Work Step by Step

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