You have to judge how steeply to attack things like tracks, ruts and even sidewalk edges. Wider tires help with some of them. My mountain bike hardly ever had any problems. My hybrid I have to be more cautious. If you can find a suitable spot you might dismount, walk over to the tracks and "walk" your tire across them at various angles to find an optimal angle for crossing.

I fell over once when moving from the street to the sidewalk. Misjudged the driveway edge. It happens. Glad you weren't hurt.