Let $f(x)=x^2+x$ for all real $x$. There exist positive integers $m$ and $n$, and distinct nonzero real numbers $y$ and $z$, such that $f(y)=f(z)=m+\sqrt{n}$ and $f(\frac{1}{y})+f(\frac{1}{z})=\frac{1}{10}$. Compute $100m+n$.

[i]Proposed by Luke Robitaille[/i]