A few years back, RW published Bruce Tulloh's 100 steps to fitness, with step 100 being "run 10m in 60 mins". I can't remember the other 99, but there were lots of intermediate goals. The idea was that in order to run 10 in 60, you have to run 4 in 24 first. Then train to run 5 in 30. Then 10k in 37. And so on.
In other words, you have to put in the speedwork to get quick, plus some regular longer runs to get the stamina up.
Once you can knock out 5 in 30 without trying, then 10 in 60 is realistic. Otherwise you may wish to have a different target.