Let \( A \), \( B \) and \( C \) be three points on the parabola \( y^2 = 6x \) and let the line segment \( AB \) meet the line \( L \) through \( C \) parallel to the \( x \)-axis at the point \( D \). Let \( M \) and \( N \) respectively be the feet of perpendiculars from \( A \) and \( B \) on \( L \). Then \( \left(\frac{AM \cdot BN}{CD}\right)^2 \) is equal to ________.
