It seems to me that abilities like "summon an X" will last beyond the duration of Cunning Brilliance, because the ability was to summon it, and you did that in the minute time. Likewise, gaining the ability to cast a specific spell or Sp ability might go away after a minute, but the spell itself won't go away.
But for stuff like Still Mind and would go away, because the bonus is the ability. It's like a permanent effect... removing the ability again removes the bonus.
With that said... Advanced Learning just adds a spell to your spell list. It functions much like an instantaneous effect. That could theoretically be permanent (it would matter for spells that require experience costs) but that seems sketchy at best. I'd say in the end it's just stuff like spells, Sp abilities, and such that you can keep past the one minute, while permanent bonuses won't stay.
JaronK