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The diagram shows the curve \(y = x ^ { 3 } \ln x\), for \(x > 0\), and its minimum point \(M\).
- Find the exact coordinates of \(M\).
- Find the exact area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = \frac { 1 } { 2 }\). [5]