This problem came up in my homework for an online class and try as I might, I can't find a solution. 

$(x-1)^3+2016(x-1)=-1$

$(y-1)^3+2016(y-1)=1$

Find $x+y$

So far, I've tried letting $(x-1)=a$ and $(y-1)=b$ and then adding the two equations and factoring out $(a+b)$ to get:

$(a+b)(a^2-ab+b^2+2016)=0$

But I don't know where to go from here.