Linux cron job (at least) every hour with random delay

I want to run a script approximately every hour but I want it with a random delay while keeping the time between the runs at least one hour.

That means:

• 00:00 01:00 + RANDOM minutes (5) => 01:05 (execution)
• 01:05 + 1 = 02:05 + RANDOM minutes (7) => 02:12 (execution)
• 02:12 + 1 = 03:12 + RANDOM minutes (2) => 03:14 (execution) ...

Is this possible using cron?