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American Idol winner David Cook opens up about the death of his older brother -- and what he hopes it offers others battling cancer.

Cook wrote a message to fans on his official website Monday, thanking them for their support one day after Adam Cook, 37, died after an 11-year struggle with brain cancer.

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"Thank you on behalf of my family and myself to everyone who has shown even the slightest bit of support to us and our efforts as a family to help eradicate this terrible affliction," he wrote, adding that he was not with his brother when he heard the news of his death Saturday night.

He had flown into Washington D.C., to take part in the 12th Annual Race for Hope 5K event on Sunday. (The rocker was the event's honorary chairman, and his team raised more the $97,000 for the cause.) Instead of flying home to be with his family, he decided to stay.

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"I decided to run in the race, despite all of this, for two reasons," Cook wrote. "First, my brother never wanted his illness to affect others. That was evident in the fact that he wanted his illness to have no part in my experience on Idol, a point he was quite adamant about. So, with that wish in mind, I ran and was involved with the event as an homage to him."

Beyond his brother, the singer participated in the charity race for the 9,000 others in attendance.

"Secondly, there are many people who are still battling, and by running and sharing my brothers story, I hope that it offers those still fighting that much more resolve to not succumb to this wretched disease," he wrote.

Cook was most thankful to those who have donated to brain cancer research.

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"I take it as affirmation that my brother was the great man that I knew, and whose ideals I constantly try to uphold in myself," he added. "It is with those ideals in tow that I vow to continue to speak out in hopes of raising whatever necessary to help eliminate cancer entirely."

In the spirit of his late brother's refusal to let his illness affect his family, Cook said that all shows -- besides a Toledo, Ohio, concert on May 6 -- will go on as scheduled.