Basically, whoever hits 60 first wins. You can add 6 at a time with a minimum of 1, therefore, if you ever have 53, you're in a losing position, since if you add 1, your opponent will have 54 and can win by adding 6 on their next turn, since we know that whoever has 53 on their turn loses, we can also extrapolate that whoever has 46 on their turn loses, since they can then be forced into having 53. We can continue this trend downwards by removing seven each time, meaning the losing numbers are: 53, 46, 39, 32, 25, 18, 11, 4. Now, if I remember correctly you don't have the first turn, but it doesn't matter as your opponent doesn't play perfectly at the start of the game. All you need to do is at the first opportunity, pick a number that will add to one of the numbers in that list, after that, she will be forced to pick a number that will allow you to pick a number that will be in the list, at which point you can simply keep picking numbers to get to one in the list, which will end with her being forced into having 53, and you have a guaranteed win.
It's been a while since I've played so if I may have gotten the amount it takes to win or the amount you can add each turn wrong.