8 In this question you must show detailed reasoning. The diagram shows part of the graph of \(y = 2 x ^ { \frac { 1 } { 3 } } - \frac { 7 } { x ^ { \frac { 1 } { 3 } } }\). The shaded region is enclosed by the curve, the \(x\)-axis and the lines \(x = 8\) and \(x = a\), where \(a > 8\).
\includegraphics[max width=\textwidth, alt={}, center]{efde7b10-b4f3-469f-ba91-b765a16ea835-5_577_1164_477_438} Given that the area of the shaded region is 45 square units, find the value of \(a\).