$f(x)=\{\begin{array}{cc}a{e}^x+bx,& x<mn>0</mn>\\ m,& x=0\\ e^{-\frac{1}{x^2}}+\sqrt[3]{x+5},& x>0\end{array}$

Determine the value of $a,b,$ and $m,$ assuming that the function $f(x)$ is differentiable everywhere. Value of $a=,b=,$ and $m=$