Is there a way to convert Corel Draw files from version 11 to X3?

You simply open it in a newer version of Corel Draw, next time you save it it will be saved as this new version.

This way you preserve the layers, objects, groups, efects, etc.

I am adding this part sometime later because some people keep asking this variation: What if I do not have this new version?

If you do not have a newer version... you do not need a newer version.

I am asuming sometimes a client want a specific version. For example "the ultimate latest version".

You do not need to do anithing. He can just open the file and that is it.