11.(2023春•大祥区校级期末)若cos(π6−α)=35\cos (\frac{\pi }{6}-\alpha )=\frac{3}{5}cos(6π−α)=53,则sin(2α+π6)=\sin (2\alpha +\frac{\pi }{6})=sin(2α+6π)=___−725-\frac{7}{25}−257___.