A day after Android 5.1.1 update was available as a factory image — which are pretty handy installing, and damn useful for restoring device back to stock — for the Project Fi devices, now, Google has made available the 5.1.1 update for regular Nexus 6 sets too.
The build no. is LMY47Z, and upon installing this factory image, which is compatible with all Nexus 6 sets except that at T-Mobile, your device will be running Android 5.1.1 — latest Android version released as of now. Download the 5.1.1 update here.