# Expression manipulation with exponential

I have the following expression

a + b + c + x + y + z + r*E^m + s/E^m + t*E^n + u/E^n


I want to extract the coefficients of exponential terms as well as the constants as a whole.

My output should be something like

{a + b + c + x + y + z,r,s,t,u}


I tried with

Coefficient[a + b + c + x + y + z + r*E^m + s/E^m + t*E^n + u/E^n,{E^m,E^-m,E^n,E^-n}]


But it only gave

{r, s, t, u}


Coefficient[a + b + c + x + y + z + r*E^m + s/E^m + t*E^n + u/E^n,E,{0,m,-m,n,-n}] // Print