In addition to registering the ADO.NET provider, you need to register the Entity Framework provider:
<entityFramework>
<providers>
<provider invariantName="MySql.Data.MySqlClient"
type="MySql.Data.MySqlClient.MySqlProviderServices, MySql.Data.Entity" />
</providers>
</entityFramework>
You also need to ensure that the provider has been built against Entity Framework 6. See this article for more information on this.