Evaluate $\int_1^\infty \frac {dx}{x^3+1}$

I would like some help with the following integral.

I would like to find a contour line to evaluate $$\int_1^\infty \frac {dx}{x^3+1}$$

So one can see that on any circumference it goes to $0$, but how do I connect it to $1$?

I have tried a number of things but without results. Can somebody offer any help?