You need a slightly different sentence. She can not only eat well but can also sleep well. 'cannot', however, can't be used there because not negates only rather than can.
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Thein Lwin 7291In this sentence, should we use 'cannot' instead of 'can not'?Use neither!
teechrThe operation was a great success. Now, not only does/can she eat well, she also sleeps well.Yes, the inversion is fine and is often added for emphasis, but it is certainly not required.