Carl Perkins' "I Care"

Between yester-day and to-day, I listened to a two-disc compilation album of Carl Perkins called The Fabulous Carl Perkins.  The first two lines of "I Care" sounded really familiar - "Now you got me started / Don't you leave me broken-hearted."  It wasn't too hard to place these as lines that also appear in Cliff Richard's "Too Much" because I had just listened to a Cliff Richard compilation album a few days ago.

But I'm not sure what to make of these two lines' appearing identically in two different songs.  "I Care" is from 1957, and "Too Much" is from 1959, so if one was influenced by the other, it would be "Too Much" influenced by "I Care."  But I don't really think that's the case here.  I think it's just a weird coincidence that illustrates that a lot of the songs from the 1950s use a lot of the same elements.  I think rhyming started and broken-hearted was just pretty common back then, and the rest of the lines for these two songs just happened to be filled in with the same words.