Integrating multiple LiDAR sensors can significantly enhance a robot's perception of the environment, enabling it to capture adequate measurements for simultaneous localization and mapping (SLAM). Indeed, solid-state LiDARs can bring in high resolution at a low cost to traditional spinning LiDARs in robotic applications. However, their reduced field of view (FoV) limits performance, particularly indoors. In this paper, we propose a tightly-coupled multi-modal multi-LiDAR-inertial SLAM system for surveying and mapping tasks. By taking advantage of both solid-state and spinnings LiDARs, and built-in inertial measurement units (IMU), we achieve both robust and low-drift ego-estimation as well as high-resolution maps in diverse challenging indoor environments (e.g., small, featureless rooms). First, we use spatial-temporal calibration modules to align the timestamp and calibrate extrinsic parameters between sensors. Then, we extract two groups of feature points including edge and plane points, from LiDAR data. Next, with pre-integrated IMU data, an undistortion module is applied to the LiDAR point cloud data. Finally, the undistorted point clouds are merged into one point cloud and processed with a sliding window based optimization module. From extensive experiment results, our method shows competitive performance with state-of-the-art spinning-LiDAR-only or solid-state-LiDAR-only SLAM systems in diverse environments. More results, code, and dataset can be found at \href{https://github.com/TIERS/multi-modal-loam}{https://github.com/TIERS/multi-modal-loam}.