As @Michal_Adamaszek has shown,
x*log(1+x/y) = rel_entr(x+y,y) + rel_entr(y,x+y) , which is convex (not concave).
So if your post has a typo and is supposed to have x/y rather than 1/y, here is the formulation to use. Otherwise, you’re out of luck with CVX, as @jackfsuia says.