fungus:
If it can do 86 amps for 5 seconds then it can do 20mA for about six hours...but that's to discharge to half voltage so your LED would be dim. If you run at 10mA you might be OK but it would take two connected in series to keep your LED at 20mA all night.
For a capacitor, the fundamental equation is Q = CV where C is the capacitance, V is the change in voltage, and Q is charge. If the current is constant, then Q can be replace by It, where I is current and t is time. So if you charge your 400F capacitor to some known voltage and then discharge it at a constant 20mA, it will take (400 * 1)/0.02 = 20000 seconds (about 5h30min) for the voltage to drop by 1v.
In practice, to drive any LED other than a red one, you would need to use a boost converter.