Android 5.1.1 has been around for some time now and a few days ago factory images were even made available for the Nexus 4 and Nexus 5. Yet, Google seems to be neglecting its latest handset, the Motorola Nexus 6.
Today, however, an OTA, build on Android 5.1.1 has begun seeding to Shamu owners on T-Mobile. The news was confirmed by the carrier on Twitter and it is already present on its support page.
The package bears the build number LYZ28E and weighs about 125MB. It brings about various Android 5.1.1 features and improvements and is also bundled with T-Mobile's own WiFi calling feature. Naturally, the roll-out procedure is staged and eligible users might not get the package immediately. All unit should, however, get the update over the next couple of weeks. If you are really eager, there is always manual flashing. The package can be found in the source link.
As far as factory images of Android 5.1.1 for Nexus 6, we can only expect that they will come shortly. We will be sure to keep you updated once that happens.