How do I query Android system accessibility settings?

Android allows the user to adjust the audio balance on their device (example screenshot at http://ift.tt/1tFZo4v).

I'm creating an app that will be sending unique audio to each channel, so I need to make sure the accessibility balance setting is still at the default middle setting.

I discovered the AccessibilityManager class (http://ift.tt/1edzcEm) which states that it "provides facilities for querying the accessibility state of the system". But I'm at a loss as to how to use it to retrieve the audio balance setting.

Is AccessibilityManager the correct class to use? If so, how can I use it for my needs? If not, which class/method in the Android SDK should I use?