\(\left(x-3\right)^3+3-x=0\)
\(\Rightarrow\left(x-3\right)^3-\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left[\left(x-3\right)^2-1\right]=0\)
\(\Rightarrow\left(x-3\right)\left(x-4\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\\x=4\end{matrix}\right.\)