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 \(f(1) \).