I had a similar issue for a good two months. Green algae covered everything and I was ripping my hair out over it. I finally decided to just invest some serious effort and fight the algae problem full force.
What worked for me was to do a big clean of the tank, taking everything out that was removable and scrubbing algae off those object. I also scraped the glass and rinsed the filter elements in tank water (to preserve the good bacterias).
While doing this I was removing tank water and had it down to about 60% of normal water level. I filled it up and then did a 50% water change. So in total it was about a 65% tank water change, coupled with heavy cleaning.
My fish all took to the stresses just fine and I proceeded with phase two. Over the next week I did a DAILY 30% water change and stopped fertilization. After the first week I continued the daily water changes but dropped the amount to only 10%. After all that was done my nitrates reached a stable 5-10 ppm.
Also make sure your nitrate test is calibrated. A quick search on the forums should get you a pretty good ho-to thread on test kit calibration.