2025 IGCSE Additional Mathematics February/March 0606/12 Q10

The point \(P\) lies on the curve \(y=(5x+2)^{2/3}\).

The \(x\)-coordinate of \(P\) is \(5\).

The normal to the curve at \(P\) intersects the line \(x+y=11\) at the point \(Q\).

The point \(R\) is the reflection of \(Q\) in the tangent to the curve at \(P\).

Find the coordinates of \(R\).[9]