After reading through a lot of online resources regarding whether it is appropriate to write an addendum explaining a score difference I'm still unsure of what to do because of the mixed opinions on this topic.

I went from a 159 in December 2016 to a 179 in September 2017 (even I find this unbelievable) and I'm not sure if I should write an addendum or how I should go about explaining this and how it will affect my chances of admissions. The only explanation I have is that I didn't study adequately for the first take because I misjudged the time I needed to set aside for the test while juggling academics, an internship, and other personal problems (i.e. family illness). I was very close to cancelling the day before but I went ahead with the test anyways hoping for the best because I wanted to make the deadlines for that admissions cycle. Consequently, I had to pass on that cycle, and I stopped all LSAT studying and instead focused on school. It wasn't until July (after graduation) that I started preparing for the LSAT again, and this time I had set aside the summer to study so that I would have adequate time to prepare. I was expecting a score somewhere in the mid-170s according to my PT average but never expected to score 179 and so now I'm wondering how to go about explaining and applying with a 20 point increase (especially if I'm now aiming for the top law schools because I know they might be more skeptical about multiple scores and such a large gap)?

Any help is appreciated :)