HMMT 2008 U29

Let $(x, y)$ be a pair of real numbers satisfying

$$56 x+33 y=\frac{-y}{x^{2}+y^{2}}, \text { and } 33 x-56 y=\frac{x}{x^{2}+y^{2}}$$

Determine the value of $|x|+|y|$.