"managed to share" is correct and perfectly usable in written English.
You can use it whenever you want to express that someone succeeded in sharing something, usually an idea or experience. For example: "I managed to share some of my ideas with the group, which made me feel like I had contributed something valuable."
Tonight, he and Jefferson managed to share a few friendly words on the court.
Before he left, he managed to share some insight with his followers about his attitude to success.
— For a long time, Joe Minter managed to share a yard with his wife, Hilda, their two sons and 100,000 of their neighbors.
Two of the physician groups, Marshfield Clinic in Wisconsin and the University of Michigan Faculty Group Practice, have managed to share in the savings for all five years.
Remarkably, Australia had the highest median wealth of any country in the world – suggesting we have managed to share our national wealth more evenly than many other countries.
His fury was so comically operatic, however, that Mac managed to share a stark, neocon vision of black life without alienating his audience.
Of course, she also manages to share her love with her daugher and two grandchildren.
With these practices, patients manage to share potentially relevant pain information without accountably being heard to assert its relevance to the doctor's diagnostic inquiry.
And the overriding question of this evening was always going to be how nicely these 13 creative egos would manage to share the stage.
They called them "ribs" or "bones". I'm fascinated by the ways people under repressive regimes still manage to share information — and joy.
And there are some memorable special-effects episodes, notably one involving Jack's stomach acid and another in which Jack and Tuck manage to share a drink.
