Nested Squareroot

Calculus Level 2

Consider the function

$f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}.$

If the gradient of the tangent of the function at $x = 12$ can be expressed as $\frac{a}{b},$ where $a$ and $b$ are coprime positive integers, what is the value of $a + b?$ .