The diagram shows the curve with equation \(y= \dfrac{6}{\sqrt{3x-2}}\). The region \(R\), shaded in the diagram, is bounded by the curve and the lines \(x = 1,\) \(x = a\) and \(y = 0,\) where \(a\) is a constant greater than 1. It is given that the area of \(R\) is 16 square units.

Find the value of \(a\) and hence find the exact volume of the solid formed when \(R\) is rotated completely about the \(x\)-axis.

**Input the nearest integer to the value of the volume as your answer.**

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