The POTW High School Painting Club has \(30\) student members, some from Grade \(11\) and the remainder from Grade \(12\). Over the year, they want to fundraise money for the school art department. Each possible pairing of students from the club will create exactly one painting together. When two Grade \(11\) students paint together, they will sell the painting for \(\$20\). When a Grade \(11\) and a Grade \(12\) student paint together, they will sell the painting for \(\$30\). When two Grade \(12\) students paint together, they will sell the painting for \(\$40\).
When all the paintings are sold, the students will have raised \(\$13\,920\). How many of the \(30\) members of the club are Grade \(11\) students?