^Yah Keith Miller certainly had a lot of responsibility. He batted #5 and opened the bowling. Very few of the great ARs have done that. Sobers and Kallis weren't good enough bowlers to open, and Botham and Imran batted further down for most of their careers.
This is the page you are after:
Records | Test matches | All-round records | A hundred and five wickets in an innings | ESPN Cricinfo
For those who are too lazy, only 4 players have done it more than once:
5 times - Ian Botham
2 times - Jacques Kallis, Garry Sobers, Mushtaq Mohammad
Another good one is 250 runs and 20 wickets in a series:
Records | Test matches | All-round records | 250 runs and 20 wickets in a series | ESPN Cricinfo
Those who have done that more than once:
3 times - Ian Botham & Garry Sobers
2 times - Keith Miller, Kapil Dev
Going by those you'd have to say Botham had the most influence on BOTH disciplines at once. Botham's also the only guy to ever have at least 10 100s and at least 10 5fers. Sobers only had 6 5fers, Kallis 5, Miller had 7.