BRONX, N.Y.—Juan Campis was sweating in the 90-plus degree heat as he whipped a white towel across a gleaming black Chevy TrailBlazer at a carwash here—one of six in the city that was unionized in recent months with help from two nonprofit community groups.

"They're the ones that kept us all together and showed us the steps we needed to take," Mr. Campis, 20 years old, said of the community groups. Workers probably wouldn't have joined the union without daily contact from the two groups, he said.

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