Non-Elementary Integration · Hard problem

Using $B(a,b)=\dfrac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$ and the reflection formula $\Gamma(s)\Gamma(1-s)=\dfrac{\pi}{\sin \pi s}$, evaluate $\displaystyle\int_0^{1}\dfrac{dx}{\sqrt[3]{1-x^3}}$. Give the answer with a rationalized denominator.