mixing signals from Cable TV and Sattelite TV in one cable.

I am receiving internet access and TV broadcasting from Times Warner Cable. Incoming cable from Time Warner goes to the splitter box at my house, where it gets splitted to different rooms in the house. My daughter wants to suscribe to the Sattlelite TV. I don't mind, but don't want to give up on my internet access from Times Warner because I am very happy with it.
If I bring cable from the sattelite dish to the main splitter box and add another splitter using it to combine to signals from the dish and from Times Warner, will it work?
dish --|
............|--splitter box
cable--|

Or both signals will interfere with each other?

Thank you.