Cyanobacteria is a bit of an opportunist. You may have fed more than usual and did not notice a small ammonia spike, or higher than normal nitrates but these can all play a factor.
Blackouts can be very effective but keep in mind that a few things will happen when you do this: firstly your plants will not grow which can lead to excess nutrients in the water which can lead to other nuisance algae. Secondly, rapid die off of cyanobacteria will release toxins into the water, including ammonia which of course can stress the fish and can trigger other types of nuisance algae. It you choose this method, it can be useful to keep up on the water changes to help dilute the nasty effects.
If it were me, I would do as I explained earlier but since the plants are also affected I would remove them and dip them into a dilute bleach solution for a few minutes then rinse well and put them back in the tank. Keep removing the cyanobacteria as you find it. if it doesn't get any worse, you know you are targeting the problem, which is really what you need to do. Prevention is better than the cure!