Ramanujan's nested radical is great! (2)

Algebra Level 5

$\large \frac{2016\sqrt{2016\sqrt[3]{2016\sqrt[4]{2016\sqrt[5]{2016\cdots}}}}}{\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\cdots}}}}}}=2016^{e+x}$

Find $x$ which satisfies the above equation.

Hint: Consider the infinite sum series of $e$

Clarification: $e \approx 2.71828$ denotes the Euler's number.