Let $f$ be a function such that $$ \sqrt {x - \sqrt { x + f(x) } } = f(x) , $$for $x > 1$. in that domain, $f(x)$ has the form $\frac{a+\sqrt{cx+d}}{b},$ where $a, b,c, d$ are integers and $a, b$ are relatively prime. find $a+b+c+d.$