6 The points \(A ( 1,1 )\) and \(B ( 5,9 )\) lie on the curve \(6 y = 5 x ^ { 2 } - 18 x + 19\).
- Show that the equation of the perpendicular bisector of \(A B\) is \(2 y = 13 - x\).
The perpendicular bisector of \(A B\) meets the curve at \(C\) and \(D\). - Find, by calculation, the distance \(C D\), giving your answer in the form \(\sqrt { } \left( \frac { p } { q } \right)\), where \(p\) and \(q\) are integers.