Non-Elementary Integration · Challenge 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 $\displaystyle\int_0^{\infty}\dfrac{dx}{1+x^3}$. Give the answer with a rationalized denominator.