Let the image of the point \( \left(\dfrac{5}{3},\dfrac{5}{3},\dfrac{8}{3}\right) \) in the plane \( x-2y+z-2=0 \) be \( P \). If the distance of the point \( Q(6,-2,\alpha),\ \alpha>0 \), from \( P \) is \( 13 \), then \( \alpha \) is equal to _____.
