For example: 暑すぎて眠れない日々が続いてる。is negative sentence(眠れない)
but 暑すぎてろくに眠れない日々が続いてる。 is positive sentence???
For example: 暑すぎて眠れない日々が続いてる。is negative sentence(眠れない)
but 暑すぎてろくに眠れない日々が続いてる。 is positive sentence???
You have the right idea that Japanese is generally logical about negation: it treats two negatives as cancelling out to a positive whenever that makes sense for the grammatical structure, and doesn't have the Romance language tendency (much weaker in English, but often seen in low-prestige dialects) of using double negation for emphasis.
However, this ろく (kanji 碌 or 陸, but normally written in kana) is not itself a negation. Its intrinsic meaning is positive, and similar to 十分. It's just that ろく is a negative polarity item, so it normally only appears in negative sentences. It modifies the kind of negation: 眠れない "couldn't sleep" -> ろくに眠れない "couldn't sleep enough".
In other words, it works the same way in a negative sentence that あまり or べつに do, although these are also used in positive sentences.
As an example of the sort of double negation you have in mind, consider しかない, which creates a positive sense of obligation or exclusivity. The isolated meaning of しか would be something like "other than", if it could be used that way.