This is called/referred to as averaging down your price per share. Yes, the total you paid out stays the same but you now have 60 additional shares that can be sold. So selling 10 shares at any given price per share opposed to selling 70 shares for the same amount, you are going to make more money selling 70 shares then if you only had 10.
How does that make sense? Here is the definition for you just in case you didn't know : http://www.investopedia.com/terms/a/averagedown.asp . When a company does a split and you are holding the stock, it does not mean you averaged down. Also, how does selling 70 shares make you more money then selling 10 at the higher price???
Using your example of $560
AAPL pre-split : 10 shares x $560 = $5600 AAPL post-split : 100 shares x $80 = $5600