You're asking the wrong question, because the answer won't help you.
Read again what
BlackST explained. Your SMART "failure" is not
causing the problem accessing the data - it's whatever the underlying reason for the SMART "failure" is, which is the cause of the loss of data access [from your story, you mention the data is now inaccessible]. Simply clearing SMART the warning won't (cannot) fix that underlying cause - still to be diagnosed - on your drive.
As a car analogy: Your car's oil pressure warning light (i.e. SMART warning) has been illuminated for a while, due to [for example] an oil leak (i.e. some kind of underlying problem); the engine [motor in US English] has eventually totally run out of oil, and it is now seized (i.e. you have lost access to some/all of the data). In this analogy, you are now asking the equivalent of whether just removing the oil pressure warning bulb (i.e. the resetting SMART warning) would allow the seized engine (i.e. your disk drive) to work correctly again.

If you had the skills / tools / experience / spare parts / etc. to diagnose & properly fix whatever underlying problem your drive has,
then resetting the SMART warning would make some sense. However those pre-requisites have not been met, so that situation does not apply for you.
You say the data is "valuable" but also "certainly not worth more than $100" which seem rather contradictory, so I don't want to give further advice which could make things worse. However that low budget almost certainly rules out the professional help which you need. Sorry that you probably won't like this news
