If you dry mount the image you will be easier it to frame if you mount it to 16x20 foamcore not 11x14 foamcore. You will also need to hinge the mat to the foamcore so the mat stays centered over the image. Before you do this, make sure there is room inside the frame you have to add the foamcore. Many off the shelf ready made frames do not have a very deep rabbet.
I agree with DLM about t-hinging but you can actually just hinge it to the back of the mat. Then the image will stay with the mat and you dont have to hinge the mat to the backing board (foamcore). I have a lot more information about how to do this and some pictures on my website here: photo mounting techniques