I've come up with 3 ideas. First, I want to say that I am American, Black, Mexican. Now for my ideas: My first idea is to have them as water benders living under the ocean. The next idea would be sand benders living deep in the desert, only able to bend glass or sand. And my favorite idea is this: Under the earth, deep underground, a group of people live - Black, White, Hispanic. No new language, just an American-looking group of people.
Their bending could involve light and dark laser bending. Without bringing racism and division like our world, there could be a war. However it starts, rather than dark nation vs. Light nation, both nations would comprise black, white, Hispanic-looking people in both nations (USA). A bagermole digs too deep, and the two groups escape to the surface. The dark nation runs after the light nation, and they discover the world above, full of benders and non-benders. It could be during Aang's time, Korra's time, or after Korra's time.
It makes sense of it being after or during Korra's time because they can link harmonic convergence to them getting their bending ability.
And those are my ideas .