Closed form for $\sum_{n=1}^\infty x^{-\frac{2\pi}{n}} e^{-2\pi n}$

Question

I need a closed form for $$ \sum_{n=1}^\infty x^{-\frac{2\pi}{n}} e^{-2\pi n}$$ where $x\in[1,\infty)$

For $x=1$ we have the sum as $$ \sum_{n=1}^\infty e^{-2\pi n}=\frac{1}{e^{2\pi}-1}$$

For $1<x<\infty$ we can write the sum as $$ \sum_{n=1}^\infty (x^{\frac{1}{n}} e^n)^{-2 \pi} $$ Any help would be appreciated. Thanks.