SSAS errors: Errors in the metadata manager. The dimension with ID of 'xxx' referenced by the 'yyy' cube, does not exist.

When deploying or processing a cube or dimension you may encounter an error similar to this:

Errors in the metadata manager. The dimension with ID of 'Student Financial Aid ~MC-Student AK', Name of 'Student Financial Aid ~MC-Student AK' referenced by the 'Student Financial Aid ~MC' cube, does not exist