Can I use C++14 in a library meant for C++11 client applications?

If I'm building a library where I assume that some "clients" of the library may only be using C++11, can I compile the library itself using C++14 for its internals? Are there API/ABI/link compatibility issues versus C++11? Is it safe to implement and build the library with C++14 as long as I avoid certain new features in the public API, and if so, what must I avoid? Or is it inherently incompatible to mix C++11 and C++14 within the final software project?

It's a cross-platform library, BTW, so I'll need to build it on Linux, OSX, and Windows.