Imo and in my experience, links from big sites like cnn does increase your site's authority - that's for sure. If you are able to get more than 1 cnn link, that would have better effect on your site's authority, but if just for a single link, and if it is not a targeted link, you will need more than 1 link to have an effect on your site, so if you have a big budget, by all mean go for it.
So if that is just a general link, your site authority will increase - but since it may not have your keyword/anchor text, then it will not immediately add a bonus to your SERP - but your SERP ranking will surely and gradually increase though, but not immediately, as site authority goes up, so does your SERP ranking.