Water changes will work much faster than anything else to bring your nitrate readings down, anything else other than finding the source of the problem and correcting it is a bandaid.
High nitrates can be very harmful, anything above 50ppm should be dealt with by water changes and by more attention to uneaten food, poop and excessive waste buildup in your filters.
Dip strip test kits are regarded by many as poor, get indvidual liquid test kits and make sure that the Ammonia test is "Salicylate" not "Nessler", the Salicylate is a two bottle test (two reagents) and the Nessler one bottle. Make sure that the "best by date" is within reasonable time period.
All you really need is the big three right now, Ammonia, Nitrite and Nitrate.