Total convergence of a function series

Let us consider the following function series:

$ $ \sum_{n=1}^{\infty} \frac{1}{n^x + n^{-x}}.$ $

It seems that there is total convergence in $ (- \infty, -1-\delta] \cup [1+ \delta, + \infty)$ for $ \delta > 0$ . Thank-you in advance for any help!