Integration Question

$\int _{ \sqrt [ 3 ]{ 6 } }^{ \sqrt [ 3 ]{ 16 } }{ \frac { { 24x }^{ 5 }-{ 12x }^{ 2 } }{ { x }^{ 6 }-{ x }^{ 3 } } dx=\ln Z }$ If the equation above is true, where $Z$ is an integer and ${ 2 }^{ n }=Z$ , find $n$ .