I am a little confused on the code first entity framework database.
I created a new DbContext and class that I will be storing in that context, like this:
You need to set your database server as (LocalDB)\MSSQLLocalDB. This is a change made to EF 6.1.1 onwards. The MSSQLLocalDB is mentioned in your parameter. More details on the change can be found here https://entityframework.codeplex.com/workitem/2246
MSSQLLocalDB is the default instance name on SQL Server 2014 whereas v11.0 is the default Instance name on SQL Server 2012