There is a space in our house where we would like to put plants in, however, the closest window is about 15ft away and only from one side. I was wondering if adding mirrors, to the darker side to reflect the light, would help.
It's not going to help. As the sun apparently moves across the sky you're going to have to track where the sun light falls into the room and position mirrors to focus the reflection on your plants. You would need something like a heliostat. The Sunflower Home Heliostat is a good example of what I mean.
Better to get plants that don't require much sunlight for that corner of the room.
I think it should work. White should also work (theoretically), and I know that for some fruits (melons) aluminium sheets are used, "to enlighten the dark side". These two last methods have the advantage that the light is diffused (instead of being converged in few points).
Sun is "diffuse" but strong, and mirror will just simulate it. On the other hand, the plant will not receive so much sun (farther for windows, less time to get direct sun to the plant), so the plant could be not be customized to receive so strong sun light (and in few points).