Prove that $\{1^m+1^n = 1^{m+n}\}$ is not regular using Myhill–Nerode Consider the alphabet $Σ = \{1, +, =\}$ and the following language, $PLUS = \{ 1^m + 1^n = 1^{m+n} \mid m, n ∈ ℕ \}$. Prove with Myhill-Nerode that PLUS is not a regular language. 


I know how I should use Myhill-Nerode here and how I should show that any two strings in the infinite set $S$ are distinguishable, but I am stuck at defining my infinite set S for this language. I tried $S = \{1^n \mid \text{$n$ is a natural number} \}$ but I don't think it works.
If $n \neq m$ then $1^m+1=1^{m+1} \in PLUS$ but $1^n+1=1^{m+1} \notin PLUS$.