Planes (advanced)

A plane passes through the intersection of the planes $\overrightarrow{r}\cdot (11\hat{i}+3\hat{j}+\hat{k})=8$‍ and $\overrightarrow{r}\cdot (9\hat{i}+6\hat{j}-\hat{k})=1$‍, and is perpendicular to the plane $\overrightarrow{r}\cdot (3\hat{i}-4\hat{j}-5\hat{k})=10$‍.