Find the values of $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ at the given point.
$2z^3 - xy + yz + y^3 - 55 = 0$, $(3, 1, 3)$
$\frac{\partial z}{\partial x}|_{(3, 1, 3)} = \frac{1}{55}$ (Type an integer or a simplified fraction.)
$\frac{\partial z}{\partial y}|_{(3, 1, 3)} = \boxed{}$ (Type an integer or a simplified fraction.)
