Non-isomorphic coarsely equivalent spaces

Question

I've been reading about uniform Roe algebras lately and in particular the rigidity problem. I know that in general $C_u^*(X)$ and $C_u^*(Y)$ being *-isomorphic doesn't necessrily imply that $X$ and $Y$ are isomorphic as coarse spaces, but rather only coarsely equivalent. I'm thus looking for an example of coarse spaces $X$ and $Y$ which have isomorphic associated Roe algebras but are not themeselves isomorphic as coarse spaces. Any help would be appreciated!