Rails same top-level URL route for organizations/user: domain.com/user and http://ift.tt/1N14gZD works the same

I'm attempting to make it so that top level-routing works from my Rails API to an Ember.js client in this manner (similar to how GitHub works, for example):

Hitting http://ift.tt/1gZKM9B would give you a user's page. This would either hit the http://ift.tt/1O88r6E endpoint or some other endpoint.

Hitting http://ift.tt/1YlepnM would give you an organization's page. This would either hit the http://ift.tt/1O88r6G endpoint or some other endpoint.

When getting a random URL, the client will obviously have no idea what type of model it's dealing with. It will just treat it as http://ift.tt/1YlepE0, where random_string is either a username or an organization_name.

I'm not quite sure how to deal with this situation. It's unclear where the responsibilities lie with client or server here. I can imagine maybe some sort of polymorphism working here, but can't connect the dots.