Such a password has about 157 bits of entropy, which is far too big to be found by any kind of brute-force approach.
Of course there are other ways that a password can be cracked, for example an attacker who breaks into the server can capture it as it is submitted. So it's still worth having a different password for each site.
> Such a password has about 157 bits of entropy, which is far too big to be found by any kind of brute-force approach.
To put this into perspective:
If you turned every grain of sand on Earth (about eight quintillion) into a computer able to test 1 trillion passwords per second, you'd need about 360 million years to exhaust half the search space and have better than even odds of guessing it.
Of course there are other ways that a password can be cracked, for example an attacker who breaks into the server can capture it as it is submitted. So it's still worth having a different password for each site.