In a triangle ABC, BC =7, AC =8, AB =α ∈ N and cos A =2/3. If 49 cos (3 C )+42=m/n, where gcd (m, n)=1, then m+n is equal to ____.

In a triangle $\displaystyle \mathrm{ABC}, \mathrm{BC}=7, \mathrm{AC}=8, \mathrm{AB}=\alpha \in \mathbf{N}$ and $\displaystyle \cos \mathrm{A}=\frac{2}{3}$. If $\displaystyle 49 \cos (3 \mathrm{C})+42=\frac{\mathrm{m}}{\mathrm{n}}$, where $\displaystyle \operatorname{gcd}(m, n)=1$, then $\displaystyle m+n$ is equal to $\displaystyle \_\_\_\_$.