Can all ink jet cartridges for printers be refilled?

there is a company near me tat refills old cartridges, but when i took mine to them they said mine wasn't suitable!
i heard you can do it with any cartridge with a DIY kit
i have seen there kits in computer shops!

would you recommend i refill them or should i just buy a new one?
Update: its lexmark

i don't know what number it takes, im printing stuff off now and the ink is low, that's what made me think of it!
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