A vector $\overrightarrow{c}$ , directed along the internal bisector of the angle between the vectors $\overrightarrow{a}=7\hat{i}-4\hat{j}-4\hat{k}$ and $\overrightarrow{b}=-2\hat{i}-\hat{j}+2\hat{k}$ with $\left|\overrightarrow{c}\right|=5\sqrt{6}$ is $\frac{\lambda }{\mu }(\hat{i}-7\hat{j}+2\hat{k})$ then $\lambda +\mu = \_\_\_\_\_(\lambda ,\mu$are relatively prime to each other)