I agree with Michael2 that the sentence as written doesn't really sound like something a native speaker would say.
It's certainly not grammatically wrong, though.
I also would tend to agree with Michael2 that the reason for this is because "enjoying oneself" isn't really something you talk about in terms of ability/potential. That said, it strikes me there are some contexts where it could have that nuance (thus making this expression seem less awkward. For example:
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Thanks to my high school teacher's creative and well-designed classes, I could (or "was able to") enjoy myself while learning English, even though I had previously hated studying it.
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Actually, I just noticed this, but another thing that perhaps is making the sentence feel awkward is the use of "enjoy myself while (doing something)". This kind of makes it sound like the enjoyment is separate from (or being derived from something other than) the action described, i.e. learning English. Usually, you talk about "enjoying (doing something)" (i.e. "I enjoyed learning English.") or "enjoying yourself (in general)", not "enjoying yourself while (doing something)".
The example sentence above, I think, would be even more natural if it was "I [could/was able to] enjoy learning English" rather than the version with "enjoy myself while".
Anyhow, I hope this helps and doesn't serve to cause more confusion.
(edited a bit for clarity)