Problem

The diagram shows part of the curve with equation $y = \frac{1}{(5x - 4)^{\frac13}}$ and the lines $x = 2.4$ and $y = 1$. The curve intersects the line $y = 1$ at the point $(1, 1)$.

Find the exact volume of the solid generated when the shaded region is rotated through $360^\circ$ about the $x$-axis.