\[\frac{\sqrt[6]{x^{6}y^{7}}}{3x\sqrt[6]{y}} = \frac{\sqrt[6]{x^{6} \cdot y^{6} \cdot y}}{3x\sqrt[6]{y}} =\]
\[x = - \frac{5}{9};\ \ y = 18:\]
\[\frac{|x| \cdot |y|}{3x} = - \frac{\text{xy}}{3x} = - \frac{y}{3} =\]
\[= - \frac{18}{3} = - 6.\]