How to use a software installed by "cargo install" (Rust)
It is really best to stick with one package manager then your setup will work.
Homebrew if it build tickes would put that in a directory which is on your path.
You are using cargo now so you need another directory on your path. That is ~/.cargo/bin if Homebrew has installed the standard cargo.
I just had to go through this for Apple Silicon on Big Sur as there isn't a release build of rust yet. The cargo documents make this hard to find. Possibly becaus of another comment that cargo builds will not update when upstream changes are made as would happen with a package manager (e.g. HomeBrew) So I suspect cargo is not meant for your use just for those developing in rust.