Nested everything

Algebra Level 3

We define $x^{x^{x^{x^{...}}}}=3$

$y=\sqrt{4{\sqrt{4{\sqrt{4{\sqrt{...}}}}}}}$

$z=\sqrt{5+\sqrt{5+{\sqrt{5+\sqrt{...}}}}}$

If $x^{3} +y+z=\frac{a+\sqrt{b}}{c}$ find $\frac{a+b}{3c}$