Study the convergence of the following series: $\sum_{n=0}^\infty \frac{ n+x^{2n}}{n^3+1}$. [closed]

I want to study the convergence of the following series: $\sum_{n=0}^\infty \frac{ n+x^{2n}}{n^3+1}$.

Applying the necessary condition, I deduce that the series cannot converge for $x^2 > 1$. In the interval (-1,1) I cannot apply any criteria because those give me 1.

How can I study the convergence of the series in that interval?