I have this exact same issue. I'm using integrated Intel HD Graphics 4600, which, while no powerhouse, is supposed to be compatible with DirectX 11. I tried it with the template as well, and SharpDX throws an exception when attempting to load the effect.
And, unfortunately, I'm already setting the graphics profile to HiDef in the Game1 constructor...
graphics.GraphicsProfile = GraphicsProfile.HiDef;
...and the issue still persists. I'm also using the latest build of MonoGame available via installer.
EDIT: Never mind, it turns out I was unwittingly calling graphics.ApplyChanges() before I set the profile to HiDef, with the result that the GraphicsDevice was still targeting Reach. Setting the graphics profile to HiDef is the solution to the SharpDX exception problem.
However, now that no exceptions are thrown, I have the new problem that my shader, which works using Reach, no longer works right when using HiDef. The screen only displays a solid color.