Task 181

The task

A cube of edge length $s > 0$ has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of $s$. [asy] size(5cm,5cm); pair A,B,C,D,E,F,G,H; A=(0,0); B=(1,0); C=(1,1); D=(0,1); E=(0.3,1.5); F=C+(E-D); G=B+(E-D); H=A+(E-D); draw(A--B--C--D--A--H--E); draw(D--C--F); draw(H--G); draw(D--E--F--G--B); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(G); dot(H); [/asy]