Clorox Regular is usually 6% bleach and is marked as such on the bottle (it will also say 5.7% Available Chlorine). Off-brand Ultra is also usually 6% though not usually marked. Off-brand Regular is 3% or less and generally should not be used. Whichever brand is used, only unscented bleach should be used and not "special-purpose" bleaches that have thickeners or other additives.
1 gallon of 6% bleach would add 2.8 ppm FC to 22,000 gallons.
1 gallon of 5.25% bleach would add 2.4 ppm FC to 22,000 gallons.
Did you actually have algae or was your water simply cloudy? If the latter, then you may just need to run your filter longer and clean it more frequently. Though algae growth is the primary reason for water turning dull, then cloudy and then green (if not fought), it isn't the only reason.
You need to measure the chlorine level and if it is dropping, even overnight, then the chlorine is fighting (oxidizing) algae so you need to keep adding more to keep up the FC level. With the CYA at 60, the shock level for fast reduction in algae is around 24 ppm. HOWEVER, the bag of shock, if it were Dichlor, as well as the tablets have both probably increased the CYA level which does NOT help at all. The 6 3" tablets of Trichlor would increase FC by 15.0 ppm but would also increase CYA by 9.1 ppm. For every 10 ppm FC added by Trichlor, it also adds 6 ppm to CYA. As for the Dichlor, it's even worse in that for every 10 ppm FC it adds, Dichlor also adds 9 ppm to CYA. Hopefully the "bag of shock" you used wasn't Dichlor and instead was Cal-Hypo. For Cal-Hypo, for every 10 ppm FC it adds, Cal-Hypo also adds 7 ppm to Calcium Hardness (CH).
Read this sticky
for clearing a pool of algae.