What if the plants were algae?
I did some of the napkin math on algae a couple years ago... The fun realization is that the physical carbon has to go somewhere. So if we're trying to sequester the average american's 14 tons a year of carbon or whatever it is these days, that means you're going to have at least 14 tons of dead algae to deal with. (And a lot more weight if the algae isn't dehydrated.). That's a lot of dead algae, which demonstrates the difficulty of the problem...
In other news, have you considered ditching your car and becoming a vegetarian? Not emitting the carbon in the first place is much easier!
Here's a real world* example:
https://www.youtube.com/watch?v=AAbyUaLN2QA
*youtuber