Convergence of $\int_{-\infty}^\infty \frac{dx}{x^3+1}$

Question

$$\int_{-\infty}^\infty \frac{dx}{x^3+1}$$

Online integral calculator says this definite integral is $\pi/3$ but my textbook says it diverges. Integrand is undefined at $x=-1$ and I don't know if we can use Cauchy principal value.