How to find the exact value of this number series $\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{(-3)^{n}}{n}$

Question

I already know that the series $$\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{(-3)^{n}}{n}$$ is convergent.

SumConvergence[((-3)^n/(3^n + (-2)^n) 1/n), n](*True*)
NSum[(1/(3^n + (-2)^n))*((-3)^n/n), {n, 1, Infinity}](*-3.09332855962*)

I want to know what to do to get its exact value. If its limit value is an irrational number that can't be expressed, I hope it can be proved.