If the shortest between the lines: \( \dfrac{x+\sqrt{6}}{2}=\dfrac{y-\sqrt{6}}{3}=\dfrac{z-\sqrt{6}}{4} \) and \( \dfrac{x-\lambda}{3}=\dfrac{y-2\sqrt{6}}{4}=\dfrac{z+2\sqrt{6}}{5} \) is \( 6 \), then the square of sum of all possible values of \( \lambda \) is:
