Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS) of non-proton nuclei (X-nuclei) typically require additional proton imaging for anatomical reference and B0 shimming. Therefore, two RF systems exist, necessitating cable traps to block the unwanted common-mode current at both Larmor frequencies of 1H and X-nuclei. This study introduces a frequency-independent dual-tuned cable trap that combines a standard solenoid cable trap with a float solenoid trap to independently tune high and low frequencies without compromising performance. The methods involved theoretical analysis, electromagnetic simulations, and bench tests. Two design approaches were evaluated: a float cable trap for 1H, a non-float cable trap for X-nuclei, and vice versa. Results showed that the design with the float trap for X-nuclei and non-float for 1H had superior performance, with high common-mode current suppression ability at both frequencies. Bench tests confirmed these findings, demonstrating effectiveness across various static fields and X-nuclei. The proposed frequency-independent dual-tuned cable trap provides a compact and efficient solution for multinuclear MRI and MRS, enhancing safety, image quality, and flexibility.