More Nested Stuff

Algebra Level 4

$\large\sqrt{ 5 + \cfrac{6}{ 7 + \sqrt{5 + \cfrac{6}{7 + \sqrt{5 + \ldots}}}}}$

Let $f(x)$ denote the least degree monic polynomial with integer coefficients with root equal to the number above. Find the value of $f(1)$ .