LOD system with Partial object culling?

I want to make a planet which is quite detailed. The player will never 'land' on the planet but they can get close enough that it takes up the whole screen and far enough away that it would look as small as a coin. Obviously it would require some LOD system with multiple versions of the model. My current dilemma is that I'm struggling to get a high level of detail when the player is close to the planet. I started looking into Frustum culling, the docs say:

Unity ensures that when rendering your objects those which are completely outside of this frustum are not displayed.

It sounds like only complete meshes can be culled, which was confirmed here: http://answers.unity3d.com/questions/1613/frustum-culling

So it seems that I could perhaps split my planet into tiny fragments. Although I suspect that would be difficult to texture correctly and also might increase draw calls.

What is the best way to have a LOD system with a very high detail level and maximum performance? (I want this to run on android)

Edit: The other important factor is the textures, a 2048x2048 texture wrapped around a sphere doesn't look so great when you're up close. Is there a way to handle this?