6．已知函数$f(x)=\left\{{\left.\begin{array}{l}{{2^{\vert x\vert }}+1,x\leqslant 0}\\ {\vert {lo{g_2}x}\vert ,x>0}\end{array}\right.}\right.$，若关于$x$的方程${f^2}(x)+\sqrt{2}m=({m+\sqrt{2}})f(x)$恰有5个不同的实根，则$m$的取值范围为$($　　$)$