The function $f\left(x\right)={\cos }^{-1}\left(\frac{2\left[\right|\sin x|+|\cos x\left|\right]}{{\sin }^{2}x+2\sin x+\frac{11}{4}}\right)$ is defined if $x$ belongs to (where $\left[·\right]$ represents the greatest integer function):

If the value of $x$ (non-integer) satisfying the equation $x+\frac{92}{x}=\left[x\right]+\frac{92}{\left[x\right]}$ is $m,$ then find $\left[m\right]$.

Where $\left[·\right]$ denotes the greatest integer function.