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

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