Well , Curves (Ctrl M) is one of the most powerful tools to whiten our backs :) in Photoshop but I think it also destroys the details sometimes.
What I want to recommend is another way, simply selecting the image with Magic Wand tool and make Tolerance about 10 or 20... After selecting your image copy and paste the selection area into another layer and fill it with pure white.
Use brush tool to paint every little point into white.
For edges , use a soft brush and make the flow and opacity about % 50 not to leave brush stains and jitters
You always have a chance to clean the over bleached areas with the eraser tool.
Thank you very much for reading.