What is different between the internal design of Java and C++ that lets C++ have multiple inheritance?

It's drilled into the newbie Java programmers that Java has no multiple class inheritance, and only multiple interface inheritance, because otherwise you run into diamond inheritance problem (Class A inherits from classes B and C, both of which implement method X. So which of those classes' implementation is used when you do a.X() call?)

Clearly, C++ successfully addressed this, since it has multiple inheritance.

What's different between the internal design of Java and C++ - (i'm guessing in the method dispatch methodology) that allows this problem to be solved in C++ but prevents in Java?