ExactTarget REST API - Error Code 10006, no details

After speaking with support, the error was due to the API key I have not having rights to the context/business unit where the Data Extension lived (I didn't set it up and from what I can tell the business unit can't be seen/edited once created). I created a new API client app in App Center with the correct business unit and this resolves the issue!

Updated link to error docs in their Marketing Cloud API (ExactTarget was renamed to Marketing Cloud when Salesforce made the acquisition)

The code now exists in their docs. It means 'there are other errors in the response' that you can check. I'm not always seeing other errors to in the response as it claims. But, when there are other errors, it is reporting (in my case) that I have a data type issue with one of my variables.