The way I played when I was growing up was that if your last stone lands in a space that has stones in it, you pick them all up and keep going until you land in an empty space. Is there a version were these are the rules? We also did no 'capturing' in our version and the game ends when there are no more stones on the whole board, not just one side.
I also grew up playing that way, and I was surprised to find out that the "standard" rules are different! I found a variant that fits that description: Kenyan Bao with laps.
"This version of Bao features "laps". When the last seed is sown, if it lands in a hollow with other seeds, the turn continues - the player picks up all the seeds from that hollow and continues to sow them."
I found it on this website: http://www.mastersgames.com/rules/mancala-rules.htm
There are so many variations of mancala; I'm sure this isn't they only one with those rules.