I don't agree that effort can only be used as an uncountable noun, though in many instances it is. Looking at your sentences: 1) I would say I did that without effort or I did that without any effort or I did that with no effort . I wouldn't use the plural there.
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teacherJapan They both think that "effort" shouldn't be used as a countable noun.If this means "shouldn't ever be used", it is a strange opinion. The word "efforts" is in common use, in the right context.