Series with Nested Exponents

Compute the exact value of:$$\sum_{k=1}^\infty \ln \left(\frac{2^{2^k}}{2^{2^k}+1}\right)$$The answer is in the form $\ln\left(\frac{\alpha}{\beta}\right)$ where $\alpha$ and $\beta$ are coprime integers. Input the value of $\alpha+\beta$.