This study presents a new deep learning approach for detecting brain cysts and cystic tumors using magnetic resonance imaging (MRI). The research utilizes six datasets containing MRI images of both pediatric and adult brains to improve classification accuracy and model reliability. The datasets include T1-weighted sagittal and T2-weighted images, with data augmentation techniques used to balance the classes. The proposed hybrid model combines convolutional neural networks, genetic algorithms (GA), and artificial neural networks (ANN) to enhance performance. The OzNet-GA-ANN model achieves remarkable accuracy: 100% for Dataset 1 (T1-weighted sagittal images), 99.06% for Dataset 2 (T2-weighted images), 98.08% for Dataset 3, 99.17% for Dataset 4, 98.66% for Dataset 5 (cystic tumor dataset), and 95.20% for Dataset 6 (augmented cystic tumor dataset). These results suggest that T1-weighted sagittal images provide better diagnostic accuracy than T2-weighted images for detecting pediatric brain cysts. Furthermore, the hybrid model performs consistently well across different datasets, demonstrating its reliability and potential for real-world applications. This study offers a promising approach for improving the classification of brain cysts and cystic tumors in medical imaging.