Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>Triangles $F G H$ and $F H J$ are inscribed in $\odot K$ with $\widehat{F G} \cong \widehat{F I} .$ Find $x$ if $m \angle 1=6 x-5,$ and $m \angle 2=7 x+4$