PS: Struggling with this one isn't a sign of "sucking a bit". It's a tough one to get out whichever way you choose.
to simplify the calculations, write
$\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=x\left(\sqrt[3]{\frac{5-x}{x-1}}+1\right)$
and use the substitution
$\displaystyle y=\sqrt[3]{\frac{5-x}{x-1}}$ so that $\displaystyle x=\frac{y^3+5}{y^3+1}$
and
$\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=\frac{y^3+5}{y^3+1}(y+1)=\frac{y^3+5}{y^2-y+1}$
now take the limit as $y\to -1$