Strange Equality Condition

Algebra Level 4

Let $x, y,$ and $z$ be real numbers satisfying $\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}=1.$

Find the maximum value of $\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}.$